A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for a common pattern underlying diverse behavioral phenomena: Words follow Zipf's law of brevity (the tendency of more frequently used words to be shorter), and conformity to this general pattern has been seen in the behavior of a number of other animals. It has been argued that the presence of this law is a sign of efficient coding in the information theoretic sense. However, no strong direct connection has been demonstrated between the law and compression, the information theoretic principle of minimizing the expected length of a code. Here, we show that minimizing the expected code length implies that the length of a word cannot increase as its frequency increases. Furthermore, we show that the mean code length or duration is significantly small in human language, and also in the behavior of other species in all cases where agreement with the law of brevity has been found. We argue that compression is a general principle of animal behavior that reflects selection for efficiency of coding.

Physical manifestations of linguistic units include sources of variability due to factors of speech production which are by definition excluded from counts of linguistic symbols. In this work, we examine whether linguistic laws hold with respect to the physical manifestations of linguistic units in spoken English. The data we analyse come from a phonetically transcribed database of acoustic recordings of spontaneous speech known as the Buckeye Speech corpus. First, we verify with unprecedented accuracy that acoustically transcribed durations of linguistic units at several scales comply with a lognormal distribution, and we quantitatively justify this ‘lognormality law’ using a stochastic generative model. Second, we explore the four classical linguistic laws (Zipf’s Law, Herdan’s Law, Brevity Law and Menzerath–Altmann’s Law (MAL)) in oral communication, both in physical units and in symbolic units measured in the speech transcriptions, and find that the validity of these laws is typically stronger when using physical units than in their symbolic counterpart. Additional results include (i) coining a Herdan’s Law in physical units, (ii) a precise mathematical formulation of Brevity Law, which we show to be connected to optimal compression principles in information theory and allows to formulate and validate yet another law which we call the size-rank law or (iii) a mathematical derivation of MAL which also highlights an additional regime where the law is inverted. Altogether, these results support the hypothesis that statistical laws in language have a physical origin.

Parallels of Zipf's law of brevity, the tendency of more frequent words to be shorter, have been found in bottlenose dolphins and Formosan macaques. Although these findings suggest that behavioral repertoires are shaped by a general principle of compression, common marmosets and golden-backed uakaris do not exhibit the law.However, we argue that the law may be impossible or difficult to detect statistically in a given species if the repertoire is too small, a problem that could be affecting golden backed uakaris, and show that the law is present in a subset of the repertoire of common marmosets.We suggest that the visibility of the law will depend on the subset of the repertoire under consideration or the repertoire size.1 This work was supported by the grant BASMATI (TIN2011-27479-C04-03) from the Spanish Ministry of Science and Innovation. We thank D. Lusseau for the opportunity to reanalyze the dolphin data (Ferrer-i-Cancho & Lusseau 2009) and S. L. Vehrencamp for making us aware of the research in ravens by Conner (1985). We are grateful to R. Dale, D. Lusseau, L. Doyle and B. Elvevåg for helpful comments.

The importance of statistical patterns of language has been debated over decades. Although Zipf 's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and genomes as a tendency of the mean size of the parts to decrease as the number of parts increases in many situations. This statistical regularity emerges also in the context of genomes, for instance, as a tendency of species with more chromosomes to have a smaller mean chromosome size. It has been argued that the instantiation of this law in genomes is not indicative of any parallel between language and genomes because (a) the law is inevitable and (b) noncoding DNA dominates genomes. Here mathematical, statistical, and conceptual challenges of these criticisms are discussed. Two major conclusions are drawn: the law is not inevitable and languages also have a correlate of noncoding DNA. However, the wide range of manifestations of the law in and outside genomes suggests that the striking similarities between noncoding DNA and certain linguistics units could be anecdotal for understanding the recurrence of that statistical law.2012 Wiley Periodicals, Inc. Complexity 18: [11][12][13][14][15][16][17] 2013 Key Words: statistical laws; language; genomes; music; non-coding DNA; Menzerath's law INTRODUCTIONA ttempts to demonstrate that statistical patterns of language have a trivial explanation have a long history that goes back at least to the research by G. A. Miller and collaborators questioning the relevance of Zipf's law for word frequencies around 1960 [1-3]. Zipf's law states that the curve that relates the frequency of a word f and its rank r (the most frequent word having rank 1, the second most frequent word having rank 2, and so on) should follow f $ r 2a [4]. Miller argued that if monkeys were chained ''to typewriters until they had produced some very long and random sequence of characters'' one would find ''exactly the same 'Zipf curves' for the monkeys as for the human authors '' [3]. Under his view, Zipf's law would be an inevitable consequence of the fact that words are made of units, e.g., letters or phonemes. The typewriter argument has been revived many times since then [5][6][7][8]. However, rigorous analyses indicate that the curves do not really look the same and the parameters of this random typing model giving a good fit to real word frequencies are not forthcoming [9,10] claim that the finding of another statistical pattern of language, Menzerath's law, is also inevitable [11]. P. Menzerath hypothesized that ''the greater the whole, the smaller its constituents'' (''Je größer das Ganze, desto kleiner die Teile'') in the context of language [12] (pp. 101). Converging research in music and genomes [13][14][15][16] suggests that Menzerath's law is a general law of natural and humanmade systems. In this article, we leave the term Menzerath-Altmann law for referring to the exact mathematical dependency that has been proposed by the quantitative linguistics traditi...

Abstract:It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind "the more parts the smaller the whole" as in angiosperms, but also relationships of the kind "the more parts the larger the whole". Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent.

In this work we consider Glissando Corpus—an oral corpus of Catalan and Spanish—and empirically analyze the presence of the four classical linguistic laws (Zipf’s law, Herdan’s law, Brevity law, and Menzerath–Altmann’s law) in oral communication, and further complement this with the analysis of two recently formulated laws: lognormality law and size-rank law. By aligning the acoustic signal of speech production with the speech transcriptions, we are able to measure and compare the agreement of each of these laws when measured in both physical and symbolic units. Our results show that these six laws are recovered in both languages but considerably more emphatically so when these are examined in physical units, hence reinforcing the so-called ‘physical hypothesis’ according to which linguistic laws might indeed have a physical origin and the patterns recovered in written texts would, therefore, be just a byproduct of the regularities already present in the acoustic signals of oral communication.

Linguistic laws constitute one of the quantitative cornerstones of modern cognitive sciences and have been routinely investigated in written corpora, or in the equivalent transcription of oral corpora. This means that inferences of statistical patterns of language in acoustics are biased by the arbitrary, language-dependent segmentation of the signal, and virtually precludes the possibility of making comparative studies between human voice and other animal communication systems. Here we bridge this gap by proposing a method that allows to measure such patterns in acoustic signals of arbitrary origin, without needs to have access to the language corpus underneath. The method has been applied to sixteen different human languages, recovering successfully some well-known laws of human communication at timescales even below the phoneme and finding yet another link between complexity and criticality in a biological system. These methods further pave the way for new comparative studies in animal communication or the analysis of signals of unknown code.

Menzerath's law, the tendency of Z, the mean size of the parts, to decrease as X, the number of parts, increases is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y /X, which would imply that Z scales with X as Z ∼ 1/X. That scaling is a very particular case of MenzerathAltmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ∼ 1/X in genomes. The most powerful test is a new non-parametric based upon the correlation ratio, which is able to reject Z ∼ 1/X in nine out of eleven taxonomic groups and detect a borderline group. Rather than a fact, Z ∼ 1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.